But the match will be remembered for all the wrong reasons after Milan goalkeeper Dida was forced to leave the pitch on a stretcher in the aftermath of the winning goal following a clash with a Celtic supporter.
The first chance of the match fell to Gary Caldwell. The big stopper brought the ball down at the back post but he pulled his left-foot effort wide of the target from six yards. Massimo Donati then forced a save from Dida with an effort from the edge of the area.
Celtic coped admirably with the threat of Milan in the opening half-hour with the Serie A side being limited to long-range efforts from Kaka and Clarence Seedorf.
But a piece of Samba magic from Kaka almost created an opening for the visitors ten minutes before the break.
The Brazilian lifted the ball over the Celtic defence with a deft touch, picking out the run of Filippo Inzhagi. But Lee Naylor was alert to the danger getting his body between the Italian and the ball.
Following a tense opening to the second period, Celtic eventually made the breakthrough from a corner kick. The ball found its way though to the back post where skipper Stephen McManus was on hand to knock the ball home from close range.
Milan were almost back on level terms minutes later when Artur Boruc fortuitously managed to get a hand to a wickedly swerving Andrea Pirlo free-kick.
However, it was an atrocious piece of officiating from German referee Markus Merk that helped Milan get back on level terms.
The ball was floating harmlessly out of play for a goal-kick when the whistler inexplicably pointed to the spot, adjudging that Naylor was guilty of a push inside the box. Kaka converted the penalty, sending Boruc the wrong way from the spot.
Just as it looked as if the match was heading for a draw, McDonald popped up to net the winner, firing home the rebound from close range after Dida failed to hold Caldwell's initial effort.
But the gloss was taken off Celtic's victory in the aftermath of the goal as a Celtic fan invaded the pitch and clashed with Dida, causing the Milan shot-stopper to leave the pitch on a stretcher.